5. Conclusions and outlook
The PSO algorithm has been subject to many different modifications in order to adapt to problems with discrete
variables. The approach which was presented in this work has shown satisfactory performance when applied to water
supply systems, especially for the optimal design of the networks provided by the Hanoi and New York City water
distribution problems. In fact, the solutions we obtained with our method are among the best results compared to
the published results of the same benchmark examples, but required a significantly lower number of iterations for its
approximation.